Abstract

Using a four-mode theoretical analysis we show that highly efficient anti-Stokes conversion in waveguides is more challenging to realize in practice than previously thought. By including the dynamics of conversion to 2nd Stokes via stimulated Raman scattering and four-wave mixing, models predict only narrow, unstable regions of highly efficient anti-Stokes conversion. Experimental results of single-pass Raman conversion in confined capillary waveguides validate these predictions. This places more stringent conditions on systems that require highly efficient single-pass anti-Stokes conversion.

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  1. P. S. J. Russel, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006).
    [CrossRef]
  2. F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
    [CrossRef] [PubMed]
  3. F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
    [CrossRef] [PubMed]
  4. F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
    [CrossRef] [PubMed]
  5. P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
    [CrossRef]
  6. S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
    [CrossRef] [PubMed]
  7. P. Rabinowitz, A. Kaldor, R. Brickman, and W. Schmidt, “Waveguide H2 Raman laser,” Appl. Opt. 15(9), 2005–2006 (1976).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
    [CrossRef]
  10. N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
    [CrossRef] [PubMed]
  11. L. Schoulepnikoff and V. Mitev, “Numerical method for the modeling of high-gain single-pass cascade stimulated Raman scattering in gases,” JOSA B 14(1), 62–75 (1997).
    [CrossRef]
  12. B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. B 7(2), 234–238 (1990).
    [CrossRef]
  13. Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137(6A), A1787–A1805 (1965).
    [CrossRef]
  14. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

2009 (1)

A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
[CrossRef]

2008 (1)

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
[CrossRef] [PubMed]

2007 (3)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
[CrossRef] [PubMed]

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (2)

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

1997 (1)

L. Schoulepnikoff and V. Mitev, “Numerical method for the modeling of high-gain single-pass cascade stimulated Raman scattering in gases,” JOSA B 14(1), 62–75 (1997).
[CrossRef]

1990 (1)

B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. B 7(2), 234–238 (1990).
[CrossRef]

1986 (1)

D. Hanna, D. Pointer, and D. Pratt, “Stimulated Raman Scattering of Picosecond Light Pulses in Hydrogen,” J. Quant. Electron. 22(2), 332–336 (1986).
[CrossRef]

1976 (1)

1965 (1)

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137(6A), A1787–A1805 (1965).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Abdolvand, A.

A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
[CrossRef]

Benabid, F.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
[CrossRef] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137(6A), A1787–A1805 (1965).
[CrossRef]

Bobbs, B.

B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. B 7(2), 234–238 (1990).
[CrossRef]

Bouwmans, G.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Brickman, R.

Carlsten, J. L.

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

Couny, F.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
[CrossRef] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Debaes, C.

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

Hanna, D.

D. Hanna, D. Pointer, and D. Pratt, “Stimulated Raman Scattering of Picosecond Light Pulses in Hydrogen,” J. Quant. Electron. 22(2), 332–336 (1986).
[CrossRef]

Imasaka, T.

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
[CrossRef] [PubMed]

Izaki, H.

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
[CrossRef] [PubMed]

Kaldor, A.

Knight, J. C.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Light, P. S.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
[CrossRef] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Meng, L. S.

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

Mitev, V.

L. Schoulepnikoff and V. Mitev, “Numerical method for the modeling of high-gain single-pass cascade stimulated Raman scattering in gases,” JOSA B 14(1), 62–75 (1997).
[CrossRef]

Murphy, S. K.

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

Muys, P.

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

Nazarkin, A.

A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
[CrossRef]

Pointer, D.

D. Hanna, D. Pointer, and D. Pratt, “Stimulated Raman Scattering of Picosecond Light Pulses in Hydrogen,” J. Quant. Electron. 22(2), 332–336 (1986).
[CrossRef]

Pratt, D.

D. Hanna, D. Pointer, and D. Pratt, “Stimulated Raman Scattering of Picosecond Light Pulses in Hydrogen,” J. Quant. Electron. 22(2), 332–336 (1986).
[CrossRef]

Rabinowitz, P.

Raymer, M. G.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

Roberts, P. J.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

Roos, P. A.

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

Russel, P. S. J.

Russell, P. St. J.

A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
[CrossRef]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

Schmidt, W.

Schoulepnikoff, L.

L. Schoulepnikoff and V. Mitev, “Numerical method for the modeling of high-gain single-pass cascade stimulated Raman scattering in gases,” JOSA B 14(1), 62–75 (1997).
[CrossRef]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137(6A), A1787–A1805 (1965).
[CrossRef]

Thienpont, H.

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

Vermeulen, N.

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

Warner, C.

B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. B 7(2), 234–238 (1990).
[CrossRef]

Zaitsu, S.

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783 (1964).

J. Lightwave Technol. (1)

J. Opt. Soc. B (2)

B. Bobbs and C. Warner, “Raman-resonant four-wave mixing and energy transfer,” J. Opt. Soc. B 7(2), 234–238 (1990).
[CrossRef]

P. A. Roos, L. S. Meng, S. K. Murphy, and J. L. Carlsten, “Approaching quantum-limited cw anti-Stokes conversion through cavity-enhanced Raman-resonant four-wave mixing,” J. Opt. Soc. B 21(2), 357–363 (2004).
[CrossRef]

J. Quant. Electron. (1)

D. Hanna, D. Pointer, and D. Pratt, “Stimulated Raman Scattering of Picosecond Light Pulses in Hydrogen,” J. Quant. Electron. 22(2), 332–336 (1986).
[CrossRef]

JOSA B (1)

L. Schoulepnikoff and V. Mitev, “Numerical method for the modeling of high-gain single-pass cascade stimulated Raman scattering in gases,” JOSA B 14(1), 62–75 (1997).
[CrossRef]

Phys. Rev. (2)

A. Nazarkin, A. Abdolvand, and P. St. J. Russell, “Optimizing anti-Stokes Raman scattering in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. 79(3), 031805 (2009).
[CrossRef]

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev. 137(6A), A1787–A1805 (1965).
[CrossRef]

Phys. Rev. Lett. (4)

N. Vermeulen, C. Debaes, P. Muys, and H. Thienpont, “Mitigating heat dissipation in Raman lasers using coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 99(9), 093903 (2007).
[CrossRef] [PubMed]

F. Couny, F. Benabid, and P. S. Light, “Subwatt threshold cw Raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber,” Phys. Rev. Lett. 99(14), 143903 (2007).
[CrossRef] [PubMed]

S. Zaitsu, H. Izaki, and T. Imasaka, “Phase-matched Raman-resonant four-wave mixing in a dispersion-compensated high-finesse optical cavity,” Phys. Rev. Lett. 100(7), 073901 (2008).
[CrossRef] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[CrossRef] [PubMed]

Science (1)

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multi-octave optical-frequency combs,” Science 318(5853), 1118–1121 (2007).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) A plot of the normalized anti-Stokes power versus the phase-gain mismatch factor, Δk / g 0 = (2k p-k a-k s) / g 0 (where g 0 is the Raman gain coefficient times the peak power, which was assumed to be 10 kW), and L is the interaction length after Roos [5] and Nazarkin [9]. High efficiencies are predicted but require long interaction lengths. (b-d) Raman simulations with varying levels of complexity. (b) Raman conversion with FWM simulation including only pump (green), Stokes (red), and anti-Stokes (blue) fields. The effect of phase matching (SRS gain g 0 = 10, Δk / g 0 = 0.5 solid lines, Δk / g 0 =0.05 dashed lines) can be seen by the increased threshold and conversion efficiency to anti-Stokes. (c) Simulation including cascaded SRS to the 2nd Stokes field (black). (d) This simulation includes full FWM interaction between all four fields and shows rapid conversion into the 2nd Stokes and pump fields.

Fig. 2
Fig. 2

(a) A simplified schematic of the experimental setup. The capillary was strapped to an aluminum block with a V-groove, (b) shows perspective view and (c) an end on view, and placed entirely inside a windowed gas cell (not shown). Cameras were used to look into the cell to image the input (d) and output (e) faces of the capillary to aid in coupling the light into the capillary.

Fig. 3
Fig. 3

The temporal profiles of Raman converted pulses for 80 psi of CO2. (a) An experimental plot showing the various Raman converted pulses with an input pulse peak power of 1.2 MW. (b) Various experimental traces in ascending input peak power levels showing the threshold for Stokes conversion, the subsequent threshold for 2nd Stokes conversion, and evidence of conversion to 3rd Stokes. (c) Numerical simulation of conditions in (a) using Eq. (1). Note the scale change on the pump as compared to (a).

Fig. 4
Fig. 4

(a) The phase-gain mismatch factor as a function of pressure for H2 assuming a 10 kW peak power. Experimental spatial mode profiles are shown for 38 and 82 psi showing that higher order spatial modes can have lower thresholds than the fundamental as it becomes phase matched. (b) The conversion efficiencies for the various Raman modes using the four mode treatment of Eq. (1). A very narrow and therefore gain sensitive region of efficient anti-Stokes conversion is seen (solid blue) as compared to the three mode treatment (dashed blue).

Equations (1)

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E a z = i k a 2 n 2 [ χ * | E p | 2 E a + ε χ * E p 2 E s * + ε 2 χ * E p E s E s 2 * ] E p z = i k p 2 n 2 [ χ * | E s | 2 E p + χ | E a | 2 E p + ε 1 χ * E s 2 E s 2 * + ε 2 * χ * E a E s 2 E s * + ε * ( χ + χ * ) E p * E s E a ] E s z = i k s 2 n 2 [ χ | E p | 2 E s + χ * | E s 2 | 2 E s + ε χ E p 2 E a * + ε 2 * χ * E a E s 2 E p * + ε 1 * ( χ + χ * ) E s * E s 2 E p ] E s 2 z = i k s 2 2 n 2 [ χ | E s | 2 E s 2 + ε 1 χ E s 2 E p * + ε 2 χ E p E s E a * ] ε = exp [ i ( 2 k p k a k s ) ] , ε 1 = exp [ i ( 2 k s k p k s 2 ) ] , ε 2 = exp [ i ( k s + k p k a k s 2 ) ] ,

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